The purpose of this study is to investigate longitudinal features of children's informal mathematical knowledge and their acquisition conditions in order to construct an education program and a teaching method of informal mathematics in early childhood education. Participants are eighty-five children who entered a kindergarten in April, 1999 and finished in March, 2002. We examined their numerical abilities using original tasks their character profiles, and development profiles using standardized diagnosis inspections. The data obtained from these tasks were collected twice, and these inspections were carried out once every school year for three years. Additionally, we evaluted children's home environments once in 2002. The main results obtained from this research were as follows.Numerical original tasks were composed of counting sets and judging the numerosity of two sets, dividing a set into two halves, Piagetian tasks of number conservation, calculation of numbers, etc. The children
… More completed these tasks almost completely except number conservation and calculation of numbers. They had acquired calculation of numbers through early chilhood and achieved addition tasks with the highest correct answer rate at about 70 percent at the last. We ascertained the children's internal situations that character profiles and development profiles showed and confirmed whether they had elder brothers or elder sisters and what kind of lessons they were doing in a class of five-years-olds. We cross-analyzed these features and their numerical abilities. Character profiles and development profiles that related to acquisition of numerical ability changed acceding to the age period. These were stability of emotion at the first stage, and then independence, and self-control which constrains feelings with reason at latter stage. Particularly, the development of speech and language was a little strongly related to acquisition of numerical ability in a class of five-year-olds. Having elder brothers or sisters was not related to acquisition of numerical ability at all in a class of three-year-olds, but were slightly related in a class of four and five-year-olds.Based on these facts, We elcidated notes to construct an education program and a teaching method of informal mathematics in group education such as kindergartens. Less